Gottfried Leibniz
Gottfried Wilhelm von Leibniz (July 1, 1646 – November 14, 1716) was a German mathematician and philosopher. He occupies a prominent place in the history of mathematics and the history of philosophy. Most scholars believe Leibniz developedcalculus independently of Isaac Newton, and Leibniz's notation has been widely used ever since it was published. It was only in the 20th century that his Law of Continuity and Transcendental Law of Homogeneity found mathematical implementation (by means of non-standard analysis). He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is the foundation of virtually all digital computers. Tossup Questions # This thinker called everything that is true of an individual substance at a particular time its "complete concept." Ramon Llull's Ars Magna inspired this man's plans for an "alphabet of human thought." This deviser of the predicate-in-notion principle has a namesake "law" concerning the identity of indiscernibles. This thinker replaced causation with his idea of "pre-established harmony." This author of a refutation of Locke's Essay Concerning Human Understanding and a Discourse on Metaphysics used the principle of sufficient reason to address the problem of evil in his Theodicy. For 10 points, name this German polymath who believed in immaterial windowless unities called monads, and wrote that God must have created the best possible world before co-discovering calculus. # This philosopher argued against the possibility of an unordered universe with the analogy of deriving a function whose graph traces over randomly drawn points. He used the example of Alexander the Great to argue that a substance was a concept complete enough to allow all of its possible predicates to be deduced from it, and that consequently, any substance mirrors the properties of the entire universe. This man argued that for any (*) identical objects, any property of one is shared by the other, which is sometimes called his law. This author of Discourse on Metaphysics divided truths into "truths of reason," which rested on the principle of contradiction, and "truths of fact" which relied on a principle he described in his correspondence with Samuel Clarke: his principle of sufficient reason. For 10 points, name this philosopher mocked by Voltaire for claiming we live in the best of all possible worlds. # This thinker posited that a list of a substance's predications make up a complete notion of the substance. His namesake law states that if two objects have exactly the same properties, then they are the same object. Those ideas are his Predicate-in-Notion Principle and his concept of the Identity of Indiscernibles. He posited the existence of simple substances that interact with each other via the Principle of (*) Pre-Established Harmony; said substances also being nonextendable, indivisible, and windowless. This author of Discourse on Metaphysics stated that everything happens for a reason, which is his Principle of Sufficient Reason. For 10 points, name this author of Monadology, who asserted that God must have created the best of all possible worlds in his Theodicy. # The statement that objects that share all properties are identical is this thinker's principle of the identity of indiscernibles. This thinker argued against the Cartesian account of substances by noting that matter is divisible, and wrote that since substances cannot interact, God has established mind and body in a "pre-established harmony." In his argument that a substance expresses the whole universe, this philosopher developed the idea of "petits perceptions," found in a book in which he represented himself as Theophilius and John Locke as Philalethe. He claimed that extension can only arise from things without extension, posting a single type of substantial form that is simple and indivisible. For 10 points, name this German philosopher who wrote New Essays on Human Understanding, Theodicy, and Monadology, the inspiration of Pangloss in Voltaire's Candide. # This thinker kept up a correspondence with Samuel Clarke until his death, and he claimed that we formulate perceptions subconsciously, which he called petites perceptions. This man claimed that a concept carries with it all of its relations to other concepts, which he called the doctrine of marks and traces. His name is sometimes appended to the principle of the identity of indiscernibles. This thinker, who satirized a John Locke title in his New Essays on Human Understanding and wrote the Theodicy, believed that everything was made up of entities that have unity, harmony, and the capacity for action. He drew harsh criticism from Voltaire, who satirized him as Dr. Pangloss in Candide. For 10 points, name this German thinker who believed in the power of monads and who developed calculus independently of Isaac Newton.